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Find the values of $p$ and $q$ for which the following system of equations has infinitely many solutions.

$(2 p − 1) x + 3 y = 5; 3 x + (q − 1) y = 2$

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p = 114, q = 85

p = 144, q = 95

p = 154, q = 135

p = 174, q = 115

answer is D.

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Detailed Solution

Given: Equations

(2 p − 1) x + 3 y − 5 = 0 3 x + (q − 1) y − 2 = 0

On comparing the given equation with standard form, we get

a 1 a 2 = 2 p − 1 3, b 1 b 2 = 3 q − 1, c 1 c 2 = − 5 − 2

For infinitely many solutions,

a 1 a 2 = b 1 b 2 = c 1 c 2

2 p − 1 3 = 3 q − 1 = 52 ⇒ 4 p − 2 = 15 and 5 q − 5 = 6

Solving the above two equations, we get

p = 174, q = 115

.
Therefore,

p = 174, q = 115

equations have infinitely many solutions.
Hence, option (4) is correct.

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